The Rudolf Steiner Archive

14. On Philosophy and Formal Logic

[ 1 ] We will have a little interlude in our lectures today. For today’s topic will not be an anthroposophical one, but rather a purely philosophical subject. As a result, this evening will inevitably take on a rather dull character. But it is perhaps a good thing that anthroposophists immerse themselves in such tedious topics from time to time, allowing them to sink in—for the simple reason that they must hear time and again that the sciences—and philosophy in particular—cannot engage with anthroposophy, since only dilettantes, who have no desire to devote themselves to serious, rigorous research and serious, rigorous thinking, concern themselves with it. Dilettantism, amateurism—that is what learned philosophers repeatedly hold against anthroposophy. Now, the lecture I gave in Stuttgart—which will be published here in print next Wednesday—will shed light from a certain perspective on how philosophy, in particular, will only be able to find the path, the bridge, to anthroposophy once it has first found its own depth within itself. This lecture will show you that the philosophers who speak of the dilettantism of the anthroposophists are simply unable to build a bridge from their supposed scientific rigor to the anthroposophy they so despise, because they lack philosophy itself—because, so to speak, they indulge in the worst kind of dilettantism within their own field.

[ 2 ] There is indeed a certain crisis in the field of philosophy. In our intellectual life today, we have a fruitful and extraordinarily significant natural science. We have also made purely scientific progress in other areas of intellectual life, thanks to the fact that positive science has succeeded in constructing precise instruments that extend into various fields, instruments capable of measuring space and revealing the smallest particles. Through this and various other means at its disposal, external research has reached a point that will be immensely expanded in the future by the impending broadening of methods. But there is also the fact that this external research is counterbalanced by a lack of philosophical education among the very people who are the researchers, so that while it is possible, with the help of today’s tools, to achieve great and formidable accomplishments in the realm of external facts, those who are specifically tasked with making these accomplishments are unable to draw conclusions from these external results for the understanding of the spirit, simply because those entrusted with the external mission of the sciences do not possess a significant level of education with regard to philosophical thinking. It is one thing to conduct research using tools and external methods in a laboratory or study, and quite another to have cultivated and trained one’s thinking to such an extent that one is able to draw valid conclusions from what one can investigate—conclusions that are then capable of shedding light on the fundamental principles of existence.

[ 3 ] There were times of philosophical depth, when those who were called to it had trained their thinking in a very special way, and when external research was not as advanced as it is today. Today, the opposite is true. Remarkably, external factual research stands in stark contrast to an inability to think and to work through philosophical concepts in the broadest sense. Indeed, we are actually dealing not only with such an inability on the part of those who are supposed to be engaged in research, but also with a certain contempt for philosophical thinking. The botanist, the physicist, and the chemist today do not even find it necessary to give the most elementary foundations of the art of thinking a second thought. When they approach their work in the laboratory or in their studies, one can say: Yes, the method actually works on its own. - Anyone who is somewhat familiar with these matters knows how the method works on its own; they know that, fundamentally, it is nothing so earth-shattering when someone makes a discovery that may be profoundly significant—for the method has been laying the groundwork for a long time. If the empirical researcher stumbles upon what really matters—if such a physicist or chemist then seeks to report on the actual underlying reasons behind what he is investigating—he begins by relying on his thinking, and the result is that something “beautiful” emerges, precisely because he is not trained in thinking at all. And through this untrained, this inwardly neglected way of thinking—which is just as characteristic of today’s scholars as it is of laypeople—we have reached a point where certain doctrines are authoritatively circulating throughout the world, which laypeople then accept credulously and regard as something that is absolutely certain, whereas in reality the very reason these doctrines arose in the first place lies solely in this so-called neglected way of thinking. Certain conclusions are drawn in an unbelievable manner.

[ 4 ] Let us consider, as an example, such a conclusion that has a certain historical significance. When a bell rings, people say to themselves: I hear a sound; I investigate it to see what its external, objective cause is. - And now they discover—in this case through precise experimentation, through something that can be objectively verified by facts—that when a sound emanates from an object, the object is, in a certain sense, vibrating internally; that when a bell rings, its metal is vibrating. It can be demonstrated through precise experimentation that when the bell vibrates, it also sets the air into certain vibrations that propagate and strike my eardrum. And as a result of these vibrations—so the conclusion is, at first glance, quite plausible!—sounds are produced. I know that when I have a string, it vibrates; I can demonstrate this in the real world by placing small paper tabs on the string, which bounce off when the string is plucked. Similarly, of course, it can be demonstrated that the string in turn causes the air to vibrate—air that then strikes my ear and produces the sound. For sound, this is something that belongs to the real world, and it’s not difficult to follow once it’s explained to you. You just need to piece together the facts and draw logical conclusions from them, and then what has been said will become clear. But now the matter goes further, and that’s where it gets really tricky. People say: Yes, we perceive sound with our ears, and light and colors with our eyes. — Now it seems to them that, because sound appears, so to speak, as an effect of something external, color, too, is the effect of something external. Fine! One could imagine the external source of color in a similar way—as something that vibrates, just as the air does with sound. And just as, let’s say, a certain pitch corresponds to a certain number of vibrations, so one could say that something is also moving at a specific frequency, which brings about this or that color. Why shouldn’t there be something out there—just as there is air pulsing against my eardrum—that vibrates, and why shouldn’t there be something that transmits these vibrations all the way to my eye, where they produce the impression of light? Of course, one cannot see or perceive through any instrument what is vibrating in this case. With sound, however, it is possible. There, it can be established that something is vibrating; with color, no—it cannot be perceived. But the matter seems so self-evident that it never occurs to anyone to doubt that something must be vibrating when we have a visual impression, just as something vibrates when we have auditory impressions. And since we cannot perceive what is vibrating there, we simply invent it. We say: The air is a dense substance that vibrates when sound is present; the vibrations of light are in the “ether.” This ether fills the entire universe. Now, when the sun sends us light, this is said to be due to the fact that the solar matter begins to vibrate, that these vibrations propagate through the ether, strike the eye, and produce the impression of light.

[ 5 ] It will also be forgotten very soon that this ether was invented in a purely fanciful way, that it was speculated into existence. That is how it played out historically. People present this with great certainty. They speak with absolute confidence about how such an ether expands and vibrates—so confidently, in fact, that the public forms the judgment: “Yes, science has established this!” How often do you hear this judgment today: “Science has established that such an ether exists, whose vibrations cause the sensations of light in our eyes.” You can even read in very nice books that everything is based on such vibrations. This goes so far that people seek the very foundations of human thought in such vibrations of the ether: A thought is the effect of the ether on the soul. What underlies it are vibrations in the brain, vibrating ether, and so on. - And so, for very many people, what they have thus conceived and speculated upon presents itself as the actual reality of the world, something that cannot be doubted at all; and yet it is based on nothing other than the error in thinking described above. You must not confuse what is called “ether” here with what we call “ether.” We are speaking here of something supernatural; physics, however, speaks of the ether as something that exists in space like any other body, to which properties are ascribed just as they are to physical bodies. One has the right to speak of something as a real fact only if one has established it, if it truly exists out there, if one can experience it. Facts must not be invented. The ether of the modern scientist is an invention—that is the crux of the matter.

[ 6 ] It is therefore, at the very foundation of our physics, a tremendous fantasy—an arbitrary invention of mysterious ether vibrations, atomic and molecular vibrations—all of which cannot possibly be accepted, because nothing can be regarded as real except what can actually be perceived. Can any such etheric vibration, as physics assumes, be perceived? We would have epistemological justification for assuming it only if we could ascertain it by the same means by which we perceive other things. We have no means of establishing things other than through sensory perception. Could it be light or color that vibrates in the ether? Impossible, for it is supposed to be the very source of color and light. Can it be perceived by other senses? Impossible; it is something that is supposed to give rise to all perceptions, yet at the same time cannot possibly be perceived by the very concept we have ascribed to it. It is something that looks very much like a knife that has neither a handle nor a blade, something in which, so to speak, the front part of the concept consumes the back part on its own. Yet something quite peculiar is happening here, and you can see in this evidence of just how justified—as bold as the expression may sound—the term “neglected” is in relation to philosophical thought. In doing so, people completely forget to take the simplest necessities of thought into account.

[ 7 ] And so, by spinning such theories, certain people come to say: Everything that appears to us—what is it other than something based on vibrating matter, vibrating ether, motion? If you were to examine everything in the world, you would find that wherever there is color and so on, there is nothing but vibrating matter. When, for example, light propagates, nothing passes from one part of space to another; nothing flows from the sun to us. - In certain circles, people imagine it this way: Between us and the sun lies the ether; the sun’s molecules are dancing; because they dance, they set the neighboring ether particles in motion; now the adjacent ones dance as well; because they dance, the next ones dance in turn, and so it continues all the way down to our eye, and when it reaches us, our eye perceives light and color. So, it is said, nothing flows downward; what dances remains up above; it merely stimulates others to dance. Only the dance propagates. There is nothing in the light itself that would flow downward. - It is as if a long line of people were standing there, each one striking the next person, who in turn passes the blow on to the third, and that person to the fourth. The first one does not move away, nor does the second; the blow propagates itself. This, it is said, is how the dance of the atoms propagates itself. In a diligently and eruditely written pamphlet—which must be acknowledged insofar as it stands at the very pinnacle of science—someone has achieved something quite clever. He wrote: The foundation of all phenomena is that nothing moves into another part of space; only the movements propagate. So when a person walks forward, it is a misconception to think that he carries his physicality over into another part of space. He takes a step, moves; the movement regenerates itself, again with the next step, and so on. This is a completely logical line of thought. But now, such a scholar should be advised—if he takes a few steps and has to regenerate himself in the next part of space, since nothing of his body comes along with him—that he must not forget to regenerate himself, otherwise he might vanish into nothingness. Here you have an example of how things lead to consequences! People just don’t draw those conclusions. What happens in public is that people say to themselves: “Well, a book has been published; someone has laid out these theories; he’s learned a great deal; and he’s come up with these ideas—and that’s a fact!”—It doesn’t occur to people that there might be something entirely different at play here.

[ 8 ] So the point is that the situation really isn’t that bad when it comes to the “dilettantism” of anthroposophy. It is true that those who stand on the same ground as intellectual scholarship can only view anthroposophy as dilettantism; but the point is that people, on their own ground, have become entangled in concepts that have become habits of thought for them. One can certainly be lenient when someone’s habits of thought lead them to have to repeat themselves over and over again; but nevertheless it must be emphasized that this side has no right to speak, from its theoretical vantage point, of the dilettantism of anthroposophy, which—if it fulfills its ideal—would certainly not be guilty of such errors as failing to attempt to draw the consequences from its premises and examine whether they are absurd. From anthroposophy, you can draw consequences everywhere. The conclusions are applicable to life, whereas there they are not—they cannot be applied to life, but apply only to the scholars’ chambers!

[ 9 ] These are the kinds of things that are meant to draw your attention to errors in reasoning, which are not readily apparent to those who do not engage with the subject. Today, the sense of authority in interactions between scholars and the public is far too strong in all circles; yet this sense of authority has little sound foundation today. One should be able to rely on it. Not everyone is in a position to follow the history of science in order to glean from it the insights that teach them about the scope of purely empirical research and intellectual inquiry. Thus, it is entirely justified, let us say, to attribute great significance to Helmholtz merely because of his invention of the ophthalmoscope. But if you trace the history of this discovery—if you can trace what already existed and how it merely remained to be discovered—you will see that it was the methods that were at work here. In fact, today one can essentially be a very minor thinker and still achieve great, monumental accomplishments, provided one has the relevant tools and their methods at one’s disposal. This is not meant to criticize all work in this field, but what has been said holds true.

[ 10 ] Now I would also like to explain to you, from a certain perspective, the reasons why all of this was able to happen. There are an immense number of such reasons; but it will suffice if we keep one or two of them in mind. If we look back at the history of intellectual life, we find that what we call the “technique of thought” and the “technique of concepts” originated in Greek intellectual life and had its first classical representative in Aristotle. He contributed something to humanity—to the scholarly community—that was undoubtedly of immense necessity to that community, yet which has since fallen into disrepute: purely formal logic. There is much public debate about whether philosophical propaedeutics should be eliminated from high school curricula. It is considered superfluous; people believe it can be studied on the side in German classes, but that it is not needed as a separate discipline. The condescending dismissal of something like the “technique of thinking” has even led to this extreme. This technique of thinking was so firmly established by Aristotle that it has made little progress. It does not need to. What has been taught in more recent times has been taught only because the very concept of logic has been lost.

[ 11 ] Now, so that you can see what is meant by this, I would like to give you an idea of formal logic. Logic is the study of concepts, judgments, and inferences. First, we must briefly discuss how concepts relate to judgments and inferences. On the physical plane, human beings initially arrive at their insights through perception. The first stage is sensation, but sensation as such would be, for example, an impression—a single color impression. However, objects do not appear to us as such isolated entities, but as combined impressions, so that we are never faced merely with individual sensations, but with combined ones—and these are perceptions. When you have an object in front of you that you perceive, you can turn your sensory organs away from the object, and an image remains within you. If this image remains, you will be able to distinguish it very clearly from the object itself. You can look at this hammer; it is perceptible to you in this way. If you turn away, an afterimage remains. We call this a mental image.

[ 12 ] It is immensely important to distinguish between perception and imagination. Things would go very well if it weren’t for the fact that, due to such a lack of thinking skills, these matters are made incredibly complicated from the very start. For example, the statement—which is advocated today in many theories of knowledge—that “we have nothing given to us but our ideas” is based on a mistake. For people say: You do not perceive the thing-in-itself. - Most people believe that behind what they perceive are dancing molecules. What they perceive is merely the impression on their own soul. Of course, since the soul is otherwise denied, it is strange that they first speak of impressions on the soul and then explain the soul as something that, in turn, consists solely of dancing atoms.

[ 13 ] When one tackles things in this way, one is reminded of the image of the brave Münchhausen, who holds himself aloft by his own hair. No distinction is made between perception and imagination. If one were to make such a distinction, one would no longer be tempted to commit this epistemological folly—which lies in saying, “The world is my imagination”—not to mention that it is already an epistemological folly to attempt to compare perception with imagination and then refer to perception as imagination. I would like someone to touch a piece of red-hot iron and then have them state that it burns. Now let them compare the idea with the perception and then say whether it burns just as much as the perception does. So the fact is that one need only approach things logically; then it becomes clear what they are all about. We must therefore distinguish between perception, in which we have an object before us, and imagination, in which this is not the case.

[ 14 ] In the realm of ideas, we again distinguish between an idea in the narrower sense and a concept. You can understand the concept of a concept by considering a mathematical concept. Imagine you draw a circle. That is not a circle in the mathematical sense. When you look at what you have drawn, you can form the idea of a circle, but not the concept. You have to imagine a point and, around it, many points that are all the same distance from that one point—the center. Then you have the concept of a circle. This mental construct is correct; what is drawn—which consists of many small chalk mounds—does not correspond to it at all. One chalk mound is farther from the center than the other.

[ 15 ] So, when you speak of a concept and a representation, you must distinguish between them in that the representation is derived from external objects, whereas the concept arises through an internal mental construction. Yet today, in countless psychology books, you can read that a concept arises solely through our abstracting from this or that which we encounter in the external world. It is believed that in the external world we encounter only white, black, brown, and yellow horses, and from these we are supposed to form the concept of a horse. Logic describes this process as follows: One sets aside what is different—first the white, black, and so on colors, then whatever else is different and again different—and finally something vague remains; this is called the concept of “horse.” One has abstracted. This, it is believed, is how concepts are formed.

[ 16 ] Those who describe the matter in this way forget that, for humanity today, the true nature of the concept can only be truly grasped through the mathematical concept, because the latter first reveals what is constructed internally and is then found again in the external world. The concept of a circle cannot be formed by going through various circles—green, blue, large, and small—and then discarding everything that is not common to them to arrive at an abstract concept. The concept is formed from within. One must construct the thought process oneself. People today simply have not yet reached the point where they can form the concept of a horse in this way. Goethe endeavored to form such inner constructions even for higher realms of natural existence. It is significant that he sought to ascend from the image to the concept. Anyone who understands the matter knows that one does not arrive at the concept of a horse by omitting the differences and retaining what remains. That is not how the concept is formed, but rather through inner construction—just like the concept of a circle—only not quite so simply. This is precisely where what I mentioned in yesterday’s lecture comes in—the wolf that eats lambs its whole life and yet never becomes a lamb. If one has the concept of the wolf in this way, one has what Aristotle calls the form of the wolf. The matter of the wolf is irrelevant. Even if it eats nothing but lambs, it will still never become a lamb. If one looked only at the matter, one would probably have to say that, since he consumes nothing but lambs, he ought actually to become a lamb. He does not become a lamb because what matters is how he organizes the matter, and that is what lives within him as the “form” and what can be constructed in the pure concept.

[ 17 ] When one combines concepts or ideas, judgments arise. If one combines the idea “horse” with the idea “black” to form “the horse is black,” one has a judgment. The combination of concepts thus forms judgments. Now, the point is that this formation of judgments is closely connected to the formal theory of concepts, which can be learned and which teaches how to combine valid concepts with one another—that is, how to form judgments. The study of this is a branch of formal logic. We will see how what I have discussed is part of formal logic. Formal logic, then, is what analyzes the inner activity of thought according to its laws—as it were, the natural history of thought—which provides us with the ability to form valid judgments and draw valid conclusions.

[ 18 ] When we come to forming a judgment here, we must once again conclude that recent philosophical work has fallen into a sort of mousetrap. For Kant stands at the gateway to recent philosophical work, and he is one of its greatest authorities. Right at the beginning of Kant’s works, we find judgments that stand in contrast to Aristotle’s. Today we want to point out how errors in thinking arise. Right at the beginning of Kant’s Critique of Pure Reason, we find discussion of analytic and synthetic judgments. What are analytic judgments supposed to be? They are those in which one concept is linked to another in such a way that the predicate concept is already contained within the subject concept and one merely extracts it. Kant says: If I conceive the concept of a body and say, “The body is extended,” this is an analytical judgment; for no one can conceive the concept of a body without conceiving it as extended. - He merely extracts the concept of the predicate from the subject. Thus, an analytic judgment is one that is formed by extracting the predicate concept from the subject concept. A synthetic judgment, on the other hand, is a judgment in which the predicate concept is not yet so embedded in the subject concept that one can simply extract it. When someone conceives of the concept of a body, they do not simultaneously conceive of the concept of heaviness. Therefore, when the concept of heaviness is added to that of the body, one has a synthetic judgment. This is a judgment that not only provides clarification but also enriches our world of thought.

[ 19 ] Now, however, you will be able to see that this distinction between analytical and synthetic judgments is not a logical one at all. For whether someone already conceives of the predicate term in connection with a subject term depends on how far they have progressed. For someone who conceives of the body as not being heavy, the concept of “heavy” is foreign in relation to the body; but for someone who, through their intellectual and other efforts, has already reached the point of conceiving of heaviness as connected to the body, all that is required is to unwrap this concept—which is entwined within their concept of “body”—and extract it. This is therefore a purely subjective distinction.

[ 20 ] In all these matters, one must proceed thoroughly. One must pinpoint the sources of error precisely. It actually seems to me that anyone who, in reality, perceives as purely subjective that which can be distilled from a concept will in fact fail to find a boundary between analytic and synthetic judgments at all—and might find themselves at a loss to provide a definition of it. What matters is something entirely different. What is it that matters? That later! It actually strikes me as quite telling what happened when these two types of judgments came up during an exam. There was a doctoral candidate who was to be examined in logic as a minor subject. He was well-versed in his main field, but knew absolutely nothing about logic. Before the exam, he told a friend that the friend should tell him a few things about logic. But the friend, who took this a bit more seriously, said: “If you still don’t know anything now, it’s wiser to just rely on your luck.”—So he took the exam. As I said, everything went very well in his major subjects; he was thoroughly prepared there. But he knew nothing about logic. The professor asked him: “So tell me, what is a synthetic judgment?” - He didn’t know the answer and was now very flustered. “Well, Candidate, don’t you know at all what that is?” the professor asked. “No!” came the reply. “An excellent answer!” exclaimed the examiner. “You see, people have been searching for so long to figure out what it is, and they still can’t figure out what a synthetic judgment actually is.” You couldn’t have given a better answer. And can you tell me, Mr. Candidate, what an analytical judgment is?” The candidate had now become bolder and replied confidently, “No!” “Oh, I see,” the professor continued, “you’ve grasped the essence of the matter. People have been searching for so long to figure out what an analytical judgment is, and they still haven’t figured it out.” No one knows. An excellent answer!” — This incident actually took place; it has always struck me—even if it shouldn’t necessarily be taken as such—as a rather good illustration of what distinguishes the two types of judgment. In fact, nothing distinguishes them; one flows seamlessly into the other.

[ 21 ] Now we must clarify how we can even speak of valid judgments in the first place, and what such a judgment is. This is a very important matter.

[ 22 ] A judgment is, at first glance, nothing more than the combination of ideas or concepts. “The rose is red” is a judgment. The question is whether the fact that such a judgment is true also makes it valid. We must realize that just because a judgment is true does not mean it is necessarily a valid judgment. Validity depends on more than simply connecting a subject term with a predicate term. Let’s take an example! “This rose is red” is a true judgment. Whether it is also valid is not a foregone conclusion; for we can also form other true judgments that are by no means valid. According to formal logic, there need be no objection to the truth of a judgment; it could be entirely true, yet its validity might still be in question. For example, someone might conceive of a creature that is half horse, one-quarter whale, and the remaining quarter camel. Let us now call this animal “Taxu.” Now, it is undoubtedly true that this animal would be ugly. The judgment “The Taxu is ugly” is therefore true and can certainly be made in accordance with all the rules of truth; for the Taxu—half horse, one-quarter whale, and one-quarter camel—is ugly; that is beyond doubt, and just as the judgment “This rose is red” is true, so too is this one. Now, one must never regard a true judgment as valid as well. Something else is necessary for that: You must be able to transform the true judgment. You must regard the true judgment as valid only when you can say, “This red rose is,” when you can incorporate the predicate back into the subject, when you can transform the true judgment into an existential judgment. In this case, then, you have a valid judgment. “This red rose is.” There is no other way than to be able to incorporate the predicate term into the subject term. Then the judgment is valid. “The taxu is ugly” cannot be made into a valid judgment. You cannot say, “An ugly taxu is.” This demonstrates the test by which one can determine whether a judgment can be made at all; it shows you how the test must be conducted. The test must be carried out by determining whether one is able to transform the judgment into an existential judgment.

[ 23 ] Here you can already see something very important that one must know: namely, that the mere combination of concepts into a logically correct judgment is not yet something that can be regarded as authoritative for the real world. Something else must be added. One must not overlook the fact that something else comes into play regarding the validity of the concept and the judgment. Something else must also be taken into account regarding the validity of our inferences.

[ 24 ] An inference is the connection between judgments. The simplest inference is: All humans are mortal. Cajus is a human — therefore: Cajus is mortal. - The major premise states: All humans are mortal; the minor premise: Cajus is a human; the conclusion: Cajus is mortal. - This syllogism is formed according to the first figure of speech, in which the subject term and the predicate term are connected by a middle term. The middle term here is “human,” the predicate term is “mortal,” and the subject term is “Cajus.” You connect them using the same middle term. Then you arrive at the conclusion: Cajus is mortal. - This conclusion is based on very specific laws. You must not alter these. As soon as you change something, you arrive at a line of reasoning that is no longer valid. No one could arrive at a correct conclusion if they were to alter it. That would not work. Because it does not work that way, you can convince yourself that thinking is based on laws. If you were to say: “The portrait is a likeness of a person; the photograph is a likeness of a person”—you could not form the conclusion from this that “The photograph is a portrait.” - It is impossible to draw a correct conclusion if you arrange the concepts differently than according to the specific laws.

[ 25 ] So you see that we have, so to speak, a genuine formal movement of concepts and judgments, and that thought is based on very specific laws. But one can never approach reality through this pure movement of concepts. In the case of the judgment, we have seen how one must first transform the true into the valid. In the case of the inference, let us convince ourselves in a different way that it is impossible to approach reality through formal inference. For an inference can be correct according to all formal laws and yet not be valid—that is, it cannot approach reality. The following example will illustrate the very simplicity of the fallacy: “All Cretans are liars,” says a Cretan. Suppose he says this. You will be able to proceed according to entirely logical figures of speech and yet arrive at an impossibility. If the Cretan says this, then—if one applies the major premise to him—he must have lied, and therefore it cannot be true. Why does this lead to a contradiction? Because you are applying the conclusion to yourself; because you are equating the subject matter with purely formal inferences—and that must not be done. Whenever one applies the formal aspects of thought to oneself, the pure formality of thought is destroyed. That is not possible.

[ 26 ] You can see from another example that the accuracy of thinking breaks down when one applies thinking to oneself—that is, when one applies what one has thought up to oneself: An elderly professor of law took on a student. It was agreed that the student would pay him a certain fee—part of it immediately and the rest only after he had won his first case. That was the agreement. The student refuses to pay the second installment. Now the law professor says to him: “You will pay me the fee under any circumstances.”—But the student insists: “I will not pay it under any circumstances.” - And he intends to do so by bringing a lawsuit against the teacher—a lawsuit over the fee. Then the teacher says: “Then you will certainly pay me; for either the judges will order you to pay—well, then you must pay—or the judges will rule that you do not have to pay, in which case you will have won the case and will therefore pay anyway.” - The student replies: “I will not pay under any circumstances; for if I win the lawsuit, the judges will grant me the right not to pay, and if I lose, then I have lost my first lawsuit, and we had already agreed that if that were the case, I would not have to pay.” - Nothing came of a completely correct formal connection because it goes back to the subject itself. That’s where formal logic always breaks down. Correctness has nothing to do with validity.

[ 27 ] The great Kant made the mistake of failing to realize that one must distinguish between truth and validity, specifically when he sought to refute the so-called ontological proof of God. This proof went something like this: If one imagines the most perfect being, this being would lack one attribute necessary for its perfection if one did not attribute existence to it. Thus, one cannot imagine the most perfect being without existence. Consequently, it exists. Kant says: This is not true, because the addition of existence to a thing does not add any further attributes. - And then he says: One hundred possible thalers—thalers conceived in thought—are neither a penny more nor a penny less than one hundred real ones. But the real ones differ considerably from the imagined ones, namely in their existence! - Thus he concludes: One can never infer existence from a concept that is merely conceived in thought. For—he argues—no matter how many imagined talers one puts in one’s wallet, they will never come into being. Therefore, one must not proceed in the same way with the concept of God by attempting to extract the concept of being from thought. —But in transferring the purely logical-formal approach from one to the other, one overlooks the fact that one must distinguish between the fact that thalers are something that can only be perceived externally, and that God is something that can be perceived internally, and that precisely in the concept of God we must disregard this property of being perceived externally. If people were to agree to pay each other with imagined talers, they would not be required to distinguish between real and imagined talers. Thus, if the being of a sensory object could be ascribed to it in thought, then the judgment would also apply to that sensory object. But one must realize that a correct judgment is not necessarily a valid one; something else must be added.

[ 28 ] So we have let some aspects of the field of philosophy pass us by today, which does no harm. It gave us a sense that the authority of today’s scientists is somewhat unfounded and that there is no need to fear when anthroposophy is portrayed as dilettantism. For what these authorities themselves have to say when they begin to move from the facts to what, through a line of reasoning, might lead to a reference to the spiritual world—that is really quite flimsy. And so today I wanted first to show you how vulnerable this way of thinking is, and then to convey the idea that there really is a science of thinking. Of course, this could only be done in broad strokes. We can go into it more deeply at a later time, but you must be prepared for the fact that this will inevitably involve a certain amount of tedium.